Project Summary The theory hub put forward in this proposal will work to translate successful and powerful approaches to describing emergent collective behavior in physical systems so they can be applied to the brain. Working closely together, the three theorists will develop methods for finding and quantifying the relevant modes of population activity in the brain, both in instantaneous snapshots of activity and activity as it evolves in time. Methods will be tested in a wide range of neural systems at different processing stages and scales: from salamanders to rodents to humans, from the retina to the cortex, from tens to thousands of cells. The approach will be validated by checking that the neural code can be read out with high fidelity even after being compressed into a much smaller subspace. The project will produce data analysis code that will be made available for neuroscience researchers to use on their own data, in addition to the results of the analyses of the particular systems studied. The neural code is inherently collective; while single neurons execute sophisticated computations, hundreds to thousands of neurons are utilized to sense the environment and drive behavior in even the simplest organisms. Although the past hundred years have yielded substantial progress in neuroscience, only recently have researchers had the capacity to record from complete neural populations - that is, to view the collective behavior of a functioning neural network. With these rapid experimental advances, there is an urgent need for complementary theoretical and computational approaches to guide the exploration of emergent behavior in large groups of neurons, allowing one to turn `big data' into `big ideas'. This proposal outlines a path towards a new theoretical framework for finding and quantitatively analyzing collective phenomena in the brain that underlie sensory coding, the representation of space, prediction, and ultimately drive behavior. The project draws heavily on the success of so-called renormalization group approaches in theoretical physics that revolutionized the understanding of collective phenomena in physical systems, and sculpted much of the progress in statistical physics in the second half of the twentieth century. The methods explored in this proposal generalize such techniques so they can be applied to a much wider range of problems. The methods developed by this theory hub based on the renormalization group will be applicable to a wide range of neural data since they are explicitly designed to generalize techniques from theoretical physics to a much broader setting. Indeed, a larger goal of the approach is to search for universality in collective behavior in the neural code. The techniques proposed are relatively straightforward to execute and will provide a fundamental methodology for interrogating high-dimensional data in fields as diverse as behavioral neuroscience and biophysics. The new techniques will also be taught as part of the three theorists' ongoing efforts to expose incoming graduate students in biological sciences to quantitative methods in biology.